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COMPARTMENTAL ANALYSIS OF DRUG DISTRIBUTION. Juan J.L. Lertora, M.D., Ph.D . Director Clinical Pharmacology Program Office of Clinical Research Training and Medical Education National Institutes of Health Clinical Center. DRUG DISTRIBUTION.

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compartmental analysis of drug distribution

COMPARTMENTAL ANALYSISOF DRUG DISTRIBUTION

Juan J.L. Lertora, M.D., Ph.D.

Director

Clinical Pharmacology Program

Office of Clinical Research Training

and Medical Education

National Institutes of Health

Clinical Center

drug distribution
DRUG DISTRIBUTION

The post-absorptive transfer of drug from one location in the body to another.

  • Compartmental Models
    • (ordinary differential equations)
  • Distributed Models
    • (partial differential equations)
pharmacokinetic models using ordinary differential equations
Pharmacokinetic Models Using Ordinary Differential Equations*

* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.

mathematical vs physical models
Mathematical vs. Physical Models*

MATHEMATICAL MODEL:

Functions or differential equations are employed without regard to the physical characteristics of the system.

PHYSICAL MODEL:

Implies certain mechanisms or entities that have physiological, biochemical or physical significance.

* Berman M: The formulation and testing of models.

Ann NY Acad Sci 1963;108:182-94

goals of drug distribution lecture
Goals of Drug Distribution Lecture
  • Significance of Drug Distribution Volumes
  • Physiological Basis of Multi-Compartment Pharmacokinetic Models
  • Clinical Implications of Drug Distribution Kinetics
volume of distribution and physiological fluid spaces
Volume of Distribution and Physiological Fluid Spaces

Intravascular Space:

None

Extracellular Fluid Space:

Inulin

Proteins and other Macromolecules

Neuromuscular Blocking Drugs (N+)

Aminoglycoside Antibiotics (initially)

volume of distribution and physiological fluid spaces9
Volume of Distribution and Physiological Fluid Spaces

Total Body Water

Urea

Ethyl alcohol

Antipyrine (some protein binding)

Caffeine

factors affecting volume of distribution estimates
Factors Affecting Volume of Distribution Estimates

Binding to Plasma Proteins

Thyroxine

Theophylline

Tissue Binding(partitioning)

Lipophilic Compounds

Digoxin(Na+ - K+ ATPase)

effect of plasma protein binding on drug distribution
Effect of Plasma Protein Binding on Drug Distribution

Cell Membranes

ICF

ECF

BINDING

PROTEINS

Elimination

effect of plasma protein binding on apparent volume of distribution
Effect of PlasmaProtein Binding on Apparent Volume of Distribution*

fu is the “free fraction”, the fraction of drug in plasma that is not bound to plasma proteins.

* Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.

impact of protein binding on thyroxine distribution volume
Impact of Protein Bindingon Thyroxine Distribution Volume*

fu=0.03%

Vd = VECF

* From Larsen PR, Atkinson AJ Jr, et al. J Clin Invest 1970;49:1266-79.

impact of protein binding on theophylline distribution volume
Impact of Protein Binding on Theophylline Distribution Volume*

fu=60%

Vd = VECF + fuVICF

* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.

basis for increased theophylline volume of distribution in pregnancy

TOTAL Vd

Basis for Increased Theophylline Volume of Distribution in Pregnancy*

* From Frederiksen MC, et al. Clin Pharmacol Ther 1986;40;321-8.

effect of plasma protein and tissue binding on the volume of distribution of most drugs
Effect of Plasma Protein and Tissue Binding on the Volume of Distribution of Most Drugs*

Ф is the ratio of tissue/plasma drug concentration.

* Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.

apparent volume of distribution for digoxin
Apparent Volume of Distribution for Digoxin

Φ includes binding to Na+-K+ ATPase.

goals of drug distribution lecture20
GOALSOF DRUG DISTRIBUTION LECTURE
  • Significance of drug distribution volumes
  • Physiologic basis of multi-compartment pharmacokinetic models
  • Clinical implications of drug distribution kinetics
first multicompartmental analysis of drug distribution
First Multicompartmental Analysis of Drug Distribution*

* FromTeorell T. Arch Intern Pharmacodyn 1937;57:205-25.

analysis of experimental data
Analysis of Experimental Data

How many compartments?

Number of exponential phases in plasma level vs. time curve determines the number ofcompartments.

compartmental analysis

Dose

k21

Central

V1

Periph.

V2

k01

k12

COMPARTMENTAL ANALYSIS

Data Equation:

C = A´e-αt+ B´e-βt

Model Equation:

dX1/dt = -(k01 + k21)X1 + k12X2

two compartment model

Dose

Central

V1

Periph.

V2

CLI

CLE

TWO-COMPARTMENT MODEL

Vd(ss) = V1 + V2

two compartment model27

Dose

Central

V1

Periph.

V2

CLI

CLE

k01

TWO-COMPARTMENT MODEL

CLE = k01V1

two compartment model28

Dose

k21

Central

V1

Periph.

V2

CLI

k12

CLE

TWO-COMPARTMENT MODEL

CLI = k21 V1 = k12 V2

intercompartmental clearance
INTERCOMPARTMENTAL CLEARANCE*

Volume-Independent Parameter Characterizing the Rate of Drug Transfer Between Compartments of a KineticModel

* FromSaperstein et al. Am J Physiol 1955;181:330-6.

is central compartment intravascular space
Is Central Compartment Intravascular Space?
  • Usually not identified as such unless drug is given rapidly IV.
  • NEED TO CONSIDER:
  • - If distribution is limited to ECF, compare the central compartment volume with plasma volume.
  • - If distribution volume exceeds ECF compare central
  • compartment with blood volume.*
  • *(account for RBC/Plasma partition if [plasma] measured)
analysis of procainamide and napa central compartment volumes
Analysis of Procainamide and NAPA Central Compartment Volumes*

* From Stec GP, Atkinson AJ Jr. J Pharmacokinet Biopharm 1981;9:167-80.

if central compartment volume is based on plasma concentration measurements
If Central Compartment Volume is Based on Plasma Concentration Measurements

RBC/P = red cell/plasma partition ratio

Hct = hematocrit

analysis of inulin kinetics with a 2 compartment model

[INULIN] (mg/dL)

AFTER INFUSION

AFTER BOLUS

MINUTES

Analysis of Inulin Kinetics with a 2-Compartment Model*

* Gaudino M. Proc Soc Exper Biol Med 1949;70:672-4.

3 compartment model of inulin kinetics

CELL MEMBRANES

3-Compartment Model of Inulin Kinetics

EXTRACELLULAR FLUID

VF

Dose

CLF

VC

CLS

VS

CLE

multicompartment model of inulin and urea kinetics

INULIN

Multicompartment Model ofInulin and Urea Kinetics*

UREA

* From Atkinson AJ Jr, et al. Trends Pharmacol Sci 1991;12:96-101.

role of transcapillary exchange
ROLE OFTRANSCAPILLARY EXCHANGE

The central compartment for both urea and inulin is the intravascular space.

Therefore, transcapillary exchange is the rate-limiting stepin the distribution of urea and inulinto the peripheral compartmentsofthe mammillary 3-compartment model.

renkin equation
RENKIN EQUATION*

Q = capillary blood flow

P = capillary permeability coefficient-surface

area product (sometimes denoted P•S).

* From Renkin EM.Am J Physiol 1953;183:125-36.

3 compartment model

Dose

VC

CLE

3-COMPARTMENT MODEL

VF

CLF = QF (1 – e PF/QF)

CLS = QS (1 – e PS/QS)

VS

for each peripheral compartment

3 UNKNOWNS:

3 EQUATIONS:

For Each Peripheral Compartment

U = urea; I = inulin

D = free water diffusion coefficient

simultaneous analysis of inulin and urea 15 n 2 kinetics45

SUBJECT 1

INULIN

UREA

SIMULTANEOUS ANALYSIS OF INULIN AND UREA-15N2 KINETICS

How does QF + QS compare with C.O.?

cardiac output and compartmental blood flows
CARDIAC OUTPUT AND COMPARTMENTAL BLOOD FLOWS*

† MEAN OF 5 SUBJECTS

* From Odeh YK, et al. Clin Pharmacol Ther 1993;53;419-25.

transcapillary exchange mechanisms
TRANSCAPILLARYEXCHANGEMechanisms
  • TRANSFER OF SMALL MOLECULES (M.W. < 6,000 Da):
    • Transfer proportional to D
  • - Polar, uncharged (urea, inulin)
    • Transfer rate < predicted from D
  • - Highly charged (quaternary compounds)
  • - Interact with pores (procainamide)
    • Transfer rate > predicted from D
  • - Lipid soluble compounds (anesthetic gases)

- Facilitated diffusion (theophylline)

theophylline intercompartmental clearance and compartmental blood flows
THEOPHYLLINEIntercompartmental Clearance and Compartmental Blood Flows*

* From Belknap SM, et al. J Pharmacol Exp Ther 1987;243:963-9.

urea and theophylline diffusion coefficients
UreaandTheophyllineDiffusion Coefficients*

* From Belknap SM, et al. J Pharmacol Exp Ther 1987;243;963-9.

goals of drug distribution lecture52
GOALSOF DRUG DISTRIBUTION LECTURE
  • Significance of drug distribution volumes
  • Physiologic basis of multi-compartment pharmacokinetic models
  • Clinical implications of drug distribution
  • kinetics
significance of drug distribution rate
SIGNIFICANCE OF DRUG DISTRIBUTION RATE

1.Affects toxicity of IV injected drugs

Theophylline, lidocaine

2. Delays onset of drug action Insulin, digoxin

3.Terminates action after IV bolus dose

Thiopental, lidocaine

pk model of theophylline distribution

SPLANCHNIC

IV Dose

CNS

CLF = QF

IVS

HEART

SOMATIC

CLS = QS

CLE

PK Model of THEOPHYLLINE Distribution

CO = QF + QS

pk pd study of insulin enhancement of skeletal muscle glucose uptake

GLUCOSE INFUSION RATE

PK-PD Study of INSULIN Enhancement of Skeletal Muscle Glucose Uptake*

* From Sherwin RS, et al. J Clin Invest 1974;53:1481-92.

distribution terminates effect bolus lidocaine dose
DISTRIBUTION TERMINATES EFFECTBOLUS LIDOCAINE DOSE*

THERAPEUTIC RANGE

* From Atkinson AJ Jr. In: Melmon KL, ed. Drug Therapeutics: Concepts for Physicians, 1981:17-33.

consequences of very slow drug distribution
CONSEQUENCES OFVERYSLOW DRUG DISTRIBUTION
  • “Flip-Flop” Kinetics
  • Effective Half-Life
  • Pseudo Dose Dependency
gentamicin elimination phase preceeds distribution phase

ELIMINATION

PHASE

DISTRIBUTION

PHASE

GENTAMICINElimination Phase Preceeds Distribution Phase*

* From Schentag JJ, et al. JAMA 1977;238:327-9.

gentamicin elimination nephrotoxic vs non toxic patient
GENTAMICIN ELIMINATION Nephrotoxic vs. Non-Toxic Patient*

NEPHROTOXIC

NON-TOXIC

* From Coburn WA, et al. J Pharmacokinet Biopharm 1978;6:179-86.

consequences of very slow drug distribution61
CONSEQUENCES OFVERYSLOW DRUG DISTRIBUTION
  • “Flip-Flop” Kinetics
  • Effective Half-Life
  • Pseudo Dose Dependency
tolrestat cumulation with repeated dosing
TOLRESTATCumulation with Repeated Dosing*

*From Boxenbaum H, Battle M: J Clin Pharmacol 1995;35:763-6.

tolrestat cumulation
TOLRESTAT CUMULATION

Predicted C.F. from T½ = 31.6 hr: 4.32

Observed C.F.: 1.29

effective half life
EFFECTIVE HALF- LIFE*

* From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:763-66.

effective half life of tolrestat

Since τ = 12 hr and Observed CF = 1.29:

EFFECTIVE HALF-LIFE OF TOLRESTAT*

* From Boxenbaum H, Battle M. J Clin Pharmacol 1995;35:763-66.

consequences of very slow drug distribution67
CONSEQUENCES OFVERYSLOW DRUG DISTRIBUTION
  • “Flip-Flop” Kinetics
  • Effective Half-Life
  • Pseudo Dose Dependency
clotting factor pharmacokinetics
CLOTTING FACTOR PHARMACOKINETICS*
  • “The Vd(ss)..... always exceeds the actual plasmavolume, implying that no drug, not even large molecular complexes as F-VIII, is entirelyconfined to the plasma space.”
  • “A too short blood sampling protocol gives flawedresults not only for terminal T1/2 but also for the model independent parameters.”

* Berntorp E, Björkman S. Haemophilia 2003;9:353-9.

topics for further study see end of chapter 3
Topics for Further Study(See end of Chapter 3)
  • Graphical Analysis of PK Data
  • Calculate Parameters of Compartmental Models
  • Comparison of Three Different Distribution Volumes